If the sequence of coefficients of a random power series has a degenerate tail field, then either its circle of convergence is a natural boundary, or this situation can be achieved by subtracting a fixed series. This generalises the known result for independent coefficient sequences.
Publié le : 1983-08-14
Classification:
Random power series,
natural boundary,
Blackwell's conjecture,
60H99,
30A12
@article{1176993530,
author = {Holgate, P.},
title = {The Natural Boundary Problem for Random Power Series with Degenerate Tail Fields},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 814-816},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993530}
}
Holgate, P. The Natural Boundary Problem for Random Power Series with Degenerate Tail Fields. Ann. Probab., Tome 11 (1983) no. 4, pp. 814-816. http://gdmltest.u-ga.fr/item/1176993530/